# PS1B - A company devises a test for the disease The test has a 5 false positive rate meaning 1 in 20 tests are positive when they should be

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Problem Set 1B: Conditional Probability and Bayes Theorem (Note: these are provided because there are no examples in the textbook. However you may expect only 1 such problem in the exam). 1. Red hair is caused by homozygosity for a recessive mutation (r) in the melanocortin receptor gene. George has brown hair and his sister has red hair. George marries Martha, a redhead (rr). (a) What is the prior probability that, if George and Martha have two children, both will be red-haired? What is the prior probability that both will be brown haired? (b) Their first child has brown hair. Given this information what is the posterior probability that George is heterozygous for the red-hair allele (Rr)? (c) Given that their first child is brown-haired, what is the probability that their second child will be red-haired? 2. A rare genetic disease affects 1 in 1000 people. This disease can be treated if it is diagnosed early, long before overt symptoms.
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Unformatted text preview: A company devises a test for the disease. The test has a 5% false positive rate, meaning 1 in 20 tests are positive when they should be negative (this is known as the test’s sensitivity, here 95%). The test does not give false negatives (the test’s specificity is 100%). If you test positive, what is the chance you actually have the disease? 3. An X-linked genetic disease can be transmitted from unaffected carrier mothers to affected sons, but can also arise from de novo mutation in the son’s X chromosome. For a given disease it has been shown that 2/3 of cases are inherited (transmitted from mother to son) and the remaining 1/3 are de novo . (a) A woman’s first child is an affected son. What is the probability that the woman is a carrier? (b) The woman has a second child, an unaffected son. What is the probability that the woman is a carrier? BICD100 Genetics Winter 2008 Chisholm...
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## This note was uploaded on 05/31/2009 for the course BICD 100 taught by Professor Nehring during the Spring '08 term at UCSD.

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